An Optimal-Order Nonconforming Multigrid Method for the Biharmonic Equation

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Previous article Next article An Optimal-Order Nonconforming Multigrid Method for the Biharmonic EquationSusanne C. BrennerSusanne C. Brennerhttps://doi.org/10.1137/0726062PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractAn optimal-order multigrid method for solving the biharmonic equation using Morley nonconforming finite elements is developed.[1] D. N. Arnold and , F. Brezzi, Mixed and nonconforming finite element methods: implementation, postprocessing and error estimates, RAIRO Modél. Math. Anal. Numér., 19 (1985), 7–32 87g:65126 0567.65078 CrossrefISIGoogle Scholar[2] Randolph E. Bank and , Todd Dupont, An optimal order process for solving finite element equations, Math. Comp., 36 (1981), 35–51 82b:65113 0466.65059 CrossrefISIGoogle Scholar[3] H. Blum and , R. Rannacher, On the boundary value problem of the biharmonic operator on domains with angular corners, Math. Methods Appl. 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Math., 50 (1987), 567–586 88e:65147 0595.65113 CrossrefISIGoogle ScholarKeywordsnonconforming multigrid methodbiharmonic equationMorley finite element Previous article Next article FiguresRelatedReferencesCited ByDetails Auxiliary Space Preconditioners for a $$C^{0}$$ Finite Element Approximation of Hamilton–Jacobi–Bellman Equations with Cordes CoefficientsJournal of Scientific Computing, Vol. 92, No. 3 | 3 August 2022 Cross Ref A fast Fourier–Galerkin method solving a system of integral equations for the biharmonic equationJournal of Integral Equations and Applications, Vol. 33, No. 4 | 1 Dec 2021 Cross Ref An Optimal Multilevel Method with One Smoothing Step for the Morley ElementComputational Methods in Applied Mathematics, Vol. 21, No. 3 | 3 June 2021 Cross Ref Code Generation for Generally Mapped Finite ElementsACM Transactions on Mathematical Software, Vol. 45, No. 4 | 25 Dec 2019 Cross Ref The least squares collocation method for the biharmonic equation in irregular and multiply-connected domainsJournal of Physics: Conference Series, Vol. 1268, No. 1 | 1 Jul 2019 Cross Ref The multigrid method for the combined hybrid elements of elasticity mechanical problemComputational and Applied Mathematics, Vol. 38, No. 2 | 5 March 2019 Cross Ref A h-Version of the Least Squares Collocation Method for the Biharmonic Equation in Irregular DomainsJournal of Physics: Conference Series, Vol. 1214 | 29 April 2019 Cross Ref Robust multigrid solvers for the biharmonic problem in isogeometric analysisComputers & Mathematics with Applications, Vol. 77, No. 1 | 1 Jan 2019 Cross Ref The least squares collocation method for biharmonic-type equations in the plate theory1 Jan 2019 Cross Ref A Fully Discrete Fast Fourier–Galerkin Method Solving a Boundary Integral Equation for the Biharmonic EquationJournal of Scientific Computing, Vol. 76, No. 3 | 26 March 2018 Cross Ref Multigrid Methods for Hellan–Herrmann–Johnson Mixed Method of Kirchhoff Plate Bending ProblemsJournal of Scientific Computing, Vol. 76, No. 2 | 17 January 2018 Cross Ref Solving the biharmonic equation in irregular domains by the least squares collocation method1 Jan 2018 Cross Ref An Augmented Method for 4th Order PDEs with Discontinuous CoefficientsJournal of Scientific Computing, Vol. 73, No. 2-3 | 23 June 2017 Cross Ref Local Multilevel Methods with Rectangular Finite Elements for the Biharmonic ProblemShibing Tang and Xuejun XuSIAM Journal on Scientific Computing, Vol. 39, No. 6 | 16 November 2017AbstractPDF (469 KB)Forty Years of the Crouzeix-Raviart elementNumerical Methods for Partial Differential Equations, Vol. 31, No. 2 | 23 July 2014 Cross Ref A ROBUST HIGH-ORDER COMPACT METHOD FOR THE THREE DIMENSIONAL NONLINEAR BIHARMONIC EQUATIONSInternational Journal of Computational Methods, Vol. 11, No. 04 | 19 August 2014 Cross Ref Optimal Solvers for Fourth-Order PDEs Discretized on Unstructured GridsShuo Zhang and Jinchao XuSIAM Journal on Numerical Analysis, Vol. 52, No. 1 | 4 February 2014AbstractPDF (425 KB)A Fast Fourier--Galerkin Method Solving a Boundary Integral Equation for the Biharmonic EquationYing Jiang, Bo Wang, and Yuesheng XuSIAM Journal on Numerical Analysis, Vol. 52, No. 5 | 16 October 2014AbstractPDF (561 KB)Local and parallel algorithms for fourth order problems discretized by the Morley–Wang–Xu element methodNumerische Mathematik, Vol. 119, No. 4 | 2 August 2011 Cross Ref C 0 Interior Penalty MethodsFrontiers in Numerical Analysis - Durham 2010 | 20 October 2011 Cross Ref Multilevel finite element preconditioning for √3 refinementMathematics of Computation, Vol. 78, No. 268 | 5 May 2009 Cross Ref A Compact Difference Scheme for the Biharmonic Equation in Planar Irregular DomainsM. 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